Detailed project
The aim of this project is to develop modelling tools for problems
involving fluid mechanics in order to explain, to control, to simulate
and possibly to predict some complex phenomena coming from physics,
chemistry, biology or scientific engineering. The complexity may
consist of the model itself, of the coupling phenomena, of the geometry
or of non-standard applications. The challenges of the scientific team
are to develop stable models and efficient adapted numerical methods in
order to recover the main physical features of the considered
phenomena. The models will be implemented into numerical codes for
practical and industrial applications.
We are interested in both high and low Reynolds number flows, interface
and control problems in physics and biology.
Our
scientific approach may be described as follows. We first determine
some reliable models and then we perform a mathematical analysis
(including stability). We then develop the efficient numerical methods,
which are implemented for specific applications.
The first goal of the project consists in modelling some complex phenomena. We combine the term model with the three following adjectives: phenomenogical, asymptotical and numerical.
Phenomenological: use of ad-hoc models in order to represent some precise phenomena. One example of such modelling process is the construction of nonlinear differential laws for the stress tensor of visco-elastic fluids. Another example is the wall law conditions in microfluidics (fluids in micro-channels) that are often taken heuristically in order to model the slip at the boundary. Finally, we also use input/output models in control theory that are useful to model the result of a process without describing it precisely.
Asymptotical: using asymptotic expansions, we derive simpler models containing all the relevant phenomena. Examples of such a process are the penalization method for the simulation of incompressible flows with obstacles or the analysis of riblets in microfluidics that are used to control the mixing of the fluids. Another example is the use of shallow fluid models in order to obtain fast predictions (Hele-Shaw approximation in microfluidics).
Numerical: direct numerical tools are used to simulate the modelized physical phenomena. A precise analysis of the models is performed to find out the most convenient numerical method in terms of stability, accuracy and efficiency. A typical example is the POD (proper orthogonal decomposition) and its use in control theory to obtain fast simulations.
Once the model has been determined, we perform its mathematical analysis. This analysis includes the effect of boundary conditions (slip conditions in microfluidics, conditions at an interface...) as well as stability issues (stability of a jet, of an interface, of coherent structures). The analysis can often be performed on a reduced model. This is the case for an interface between two inviscid fluids that can be described by a Boussinesq-type system. This analysis of the system clearly determines the numerical methods that will be used. Finally, we implement the numerical method in a realistic framework and provide a feedback to our different partners.
Our methods are used in three areas of applications.
Interface problems and complex fluids: This concerns microfluidics (bifluid flows, miscible fluids), cancer modelling, complex fluids. The challenges are to obtain reliable models that can be used by our partner Rhodia (for microfluidics) and to get tumor growth models including some mechanics.
High Reynolds flows and their analysis: We want to develop numerical methods in order to address the complexity of high Reynolds flows. The challenges are to find scale factors for turbulent flow cascades, and to develop modern and reliable methods for computing flows in aeronautics in a realistic configuration.
Control and optimization: the challenges are the drag reduction of a ground vehicle in order to decrease the fuel consummation, the reduction of turbomachinery noise emissions or the increase of lift-to-drag ratio in airplanes, the control of flow instabilities to alleviate material fatigue for pipe lines or off-shore platforms and the detection of embedded defects in materials with industrial and medical applications.
Modelling
The first goal of the project consists in modelling some complex phenomena. We combine the term model with the three following adjectives: phenomenogical, asymptotical and numerical.
Phenomenological: use of ad-hoc models in order to represent some precise phenomena. One example of such modelling process is the construction of nonlinear differential laws for the stress tensor of visco-elastic fluids. Another example is the wall law conditions in microfluidics (fluids in micro-channels) that are often taken heuristically in order to model the slip at the boundary. Finally, we also use input/output models in control theory that are useful to model the result of a process without describing it precisely.
Asymptotical: using asymptotic expansions, we derive simpler models containing all the relevant phenomena. Examples of such a process are the penalization method for the simulation of incompressible flows with obstacles or the analysis of riblets in microfluidics that are used to control the mixing of the fluids. Another example is the use of shallow fluid models in order to obtain fast predictions (Hele-Shaw approximation in microfluidics).
Numerical: direct numerical tools are used to simulate the modelized physical phenomena. A precise analysis of the models is performed to find out the most convenient numerical method in terms of stability, accuracy and efficiency. A typical example is the POD (proper orthogonal decomposition) and its use in control theory to obtain fast simulations.
Analysis and computation
Once the model has been determined, we perform its mathematical analysis. This analysis includes the effect of boundary conditions (slip conditions in microfluidics, conditions at an interface...) as well as stability issues (stability of a jet, of an interface, of coherent structures). The analysis can often be performed on a reduced model. This is the case for an interface between two inviscid fluids that can be described by a Boussinesq-type system. This analysis of the system clearly determines the numerical methods that will be used. Finally, we implement the numerical method in a realistic framework and provide a feedback to our different partners.
Applications
Our methods are used in three areas of applications.
Interface problems and complex fluids: This concerns microfluidics (bifluid flows, miscible fluids), cancer modelling, complex fluids. The challenges are to obtain reliable models that can be used by our partner Rhodia (for microfluidics) and to get tumor growth models including some mechanics.
High Reynolds flows and their analysis: We want to develop numerical methods in order to address the complexity of high Reynolds flows. The challenges are to find scale factors for turbulent flow cascades, and to develop modern and reliable methods for computing flows in aeronautics in a realistic configuration.
Control and optimization: the challenges are the drag reduction of a ground vehicle in order to decrease the fuel consummation, the reduction of turbomachinery noise emissions or the increase of lift-to-drag ratio in airplanes, the control of flow instabilities to alleviate material fatigue for pipe lines or off-shore platforms and the detection of embedded defects in materials with industrial and medical applications.
